Basic Math Examples

$A (3) = 5000 {(1 + \frac{0.299}{3})}^{n t}$

Step 1

Rewrite the equation as $5000 {(1 + \frac{0.299}{3})}^{n t} = A (3)$ .

$5000 {(1 + \frac{0.299}{3})}^{n t} = A (3)$

Step 2

Simplify.

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Step 2.1

Divide $0.299$ by $3$ .

$5000 {(1 + 0.099\overline{6})}^{n t} = A (3)$

Step 2.2

Add $1$ and $0.099\overline{6}$ .

$5000 \cdot {1.099\overline{6}}^{n t} = A (3)$

Step 3

Divide each term in $5000 \cdot {1.099\overline{6}}^{n t} = A (3)$ by $5000$ and simplify.

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Step 3.1

Divide each term in $5000 \cdot {1.099\overline{6}}^{n t} = A (3)$ by $5000$ .

$\frac{5000 \cdot {1.099\overline{6}}^{n t}}{5000} = \frac{A (3)}{5000}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5000$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5000 \cdot {1.099\overline{6}}^{n t}}{5000} = \frac{A (3)}{5000}$

Step 3.2.1.2

Divide ${1.099\overline{6}}^{n t}$ by $1$ .

${1.099\overline{6}}^{n t} = \frac{A (3)}{5000}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move $3$ to the left of $A$ .

${1.099\overline{6}}^{n t} = \frac{3 A}{5000}$

Step 4

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({1.099\overline{6}}^{n t}) = \ln (\frac{3 A}{5000})$

Step 5

Expand $\ln ({1.099\overline{6}}^{n t})$ by moving $n t$ outside the logarithm.

$n t \ln (1.099\overline{6}) = \ln (\frac{3 A}{5000})$

Step 6

Divide each term in $n t \ln (1.099\overline{6}) = \ln (\frac{3 A}{5000})$ by $t \ln (1.099\overline{6})$ and simplify.

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Step 6.1

Divide each term in $n t \ln (1.099\overline{6}) = \ln (\frac{3 A}{5000})$ by $t \ln (1.099\overline{6})$ .

$\frac{n t \ln (1.099\overline{6})}{t \ln (1.099\overline{6})} = \frac{\ln (\frac{3 A}{5000})}{t \ln (1.099\overline{6})}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $t$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{n t \ln (1.099\overline{6})}{t \ln (1.099\overline{6})} = \frac{\ln (\frac{3 A}{5000})}{t \ln (1.099\overline{6})}$

Step 6.2.1.2

Rewrite the expression.

$\frac{n \ln (1.099\overline{6})}{\ln (1.099\overline{6})} = \frac{\ln (\frac{3 A}{5000})}{t \ln (1.099\overline{6})}$

Step 6.2.2

Cancel the common factor of $\ln (1.099\overline{6})$ .

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Step 6.2.2.1

Cancel the common factor.

$\frac{n \ln (1.099\overline{6})}{\ln (1.099\overline{6})} = \frac{\ln (\frac{3 A}{5000})}{t \ln (1.099\overline{6})}$

Step 6.2.2.2

Divide $n$ by $1$ .

$n = \frac{\ln (\frac{3 A}{5000})}{t \ln (1.099\overline{6})}$